Sample Problems (and Solutions) from the 2009 International Mathematics Olympiad

Earlier this month, high school students from around the world gathered in Bremen, Germany to test their math skills in the 50th annual International Mathematics Olympiad. If you’re interested in the type of problems that high school students can solve using only algebra, geometry, number theory, take a look:

Let n be a positive integer and let

be distinct integers in the set {1, . . . , n} such that n divides for i = 1, . . . , k − 1. Prove that n does not divide .